How efficiently can one untangle a double-twist? Waving is believing!

It has long been known to mathematicians and physicists that while a full rotation in three-dimensional Euclidean space causes tangling, two rotations can be untangled. Formally, an untangling is a based nullhomotopy of the double-twist loop in the special orthogonal group of rotations. We study a particularly simple, geometrically defined untangling procedure, leading to new conclusions regarding the minimum possible complexity of untanglings. We animate and analyze how our untangling operates on frames in 3-space, and teach readers in a video how to wave the nullhomotopy with their hands.Comment: To appear in The Mathematical Intelligencer. For supplemental videos, see http://www.math.iupui.edu/~dramras/double-tip.html , or https://www.youtube.com/playlist?list=PLAfnEXvHU52ldJaOye-8kZV_C1CjxGx2C . For a supplemental virtual reality experience, see http://meglab.wikidot.com/visualizatio

Aeroelastic studies on a high-performance swept-wing airplane

Comprehensive aeroelastic analyses and wind tunnel tests have been conducted on a model of a typical high-performance airplane with swept surfaces. The investigation covered the effect of dynamic pressure upon steady state longitudinal control and stability characteristics as well as aileron effectiveness. The analysis was based upon a superposition method which yields a convergent series which may be applied to any structure on which the load is a function of the deflection. It has been shown that after a few terms this series degenerates to an elementary geometric progression which maybe summed to infinity. This conclusion is applicable even to cases where the aeroelastic effects are large and the structure is actually approaching a condition of instability. Wind tunnel tests were carried out both at the Massachusetts Institute of Technology and the California Institute of Technology. Measured data were compared with the results of the theoretical analysis

Reaping the Digital Dividend: Is it Time to Take the Great Leap?

It might be said that little of great moment has changed in academic law libraries in the past five years. Although there has been no major upheaval there have still been important developments. The trend towards online access over print which was still developing in 2001 is now unquestionable and the amount of law-related material on the Web has expanded exponentially. In itself this is a major development even though it has happened incrementally and is now taken for granted. Because of the continued growth of law material on the Web and its widespread general acceptance, we are arguably now in a position to take some radical steps which would allow us to reap the ‘digital dividend’. The ability to find, assess and retrieve relevant information is only one aspect that augurs well for the continued need for libraries and librarians. Another is the continued need which humans have to come together in a pleasant environment, to work, study and socialize. Law students are social creatures and use the law library not just because it has books. They use law libraries because they like to encounter each other, observe each other (yes, check out the talent), and work in a space that is comfortable and convenient for their other activities. Many of them live in situations which make it difficult to study. They may be parents, or live in shared accommodation. The library is a haven and refuge, and often the only place available; it must be a place to linger in, not rush through on the way to somewhere more comfortable

Fessing up to Facebook: recent trends in the use of social network websites for civil litigation

For professional “fact-gatherers” such as lawyers, insurance adjusters, claims handlers and private investigators, the vast wealth of information that people volunteer on Facebook can be a goldmine or a smoking gun, depending on your perspective. The personal information contained in a Facebook profile may be highly relevant to matters at issue in litigation; when dealing with claims, particularly in the personal injury context, the information contained on a Facebook page can make or break a case. It is, therefore, crucial that legal and insurance professionals stay informed of new developments in this emerging area of law. This article, written with the practitioner in mind, summarizes the approach currently adopted by Canadian courts and contrasts this approach with that adopted in other jurisdictions

Reaping the Digital Dividend: Is it Time to Take the Great Leap?

It might be said that little of great moment has changed in academic law libraries in the past five years. Although there has been no major upheaval there have still been important developments. The trend towards online access over print which was still developing in 2001 is now unquestionable and the amount of law-related material on the Web has expanded exponentially. In itself this is a major development even though it has happened incrementally and is now taken for granted. Because of the continued growth of law material on the Web and its widespread general acceptance, we are arguably now in a position to take some radical steps which would allow us to reap the ‘digital dividend’. The ability to find, assess and retrieve relevant information is only one aspect that augurs well for the continued need for libraries and librarians. Another is the continued need which humans have to come together in a pleasant environment, to work, study and socialize. Law students are social creatures and use the law library not just because it has books. They use law libraries because they like to encounter each other, observe each other (yes, check out the talent), and work in a space that is comfortable and convenient for their other activities. Many of them live in situations which make it difficult to study. They may be parents, or live in shared accommodation. The library is a haven and refuge, and often the only place available; it must be a place to linger in, not rush through on the way to somewhere more comfortable

A qualitative evaluation of a mentoring program for health and physical education teachers

This study examined the impact of a mentoring relationship on Quality of Work Life (QWL) and teaching self-efficacy for early career and experienced Health and Physical Education (HPE) teachers, and the application of mentoring skills by experienced teachers. Experienced mentor teachers (n = 22) were paired with early career mentee teachers (n = 22) at the beginning of a year-long intervention. Semi-structured interviews provided unanimous support for the utility of the Physical Educators Mentoring Active Teachers through Experience and Support (PE M.A.T.E.S) program and the overall impact of mentoring on professional skills, teaching self-efficacy and outcomes. Quantitative journal entries reinforced enhanced applications of mentoring skills for mentors